Can most of the basic machine learning models be easily represented as simple neural network architectures?
I think the author refers to both different choices of activation function and loss. It is explained in more detail in chapter 2. In particular 2.3 is ilustrative of this point.
I don't think there is a relation between this argument and universal approximation theorems, which state that certain classes of neural networks can approximate any function in certain domains, rather than any learning algorithm.